Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 - 22}{x + 8} = \dfrac{-2x + 26}{x + 8}$
Answer: Multiply both sides by $x + 8$ $ \dfrac{x^2 - 22}{x + 8} (x + 8) = \dfrac{-2x + 26}{x + 8} (x + 8)$ $ x^2 - 22 = -2x + 26$ Subtract $-2x + 26$ from both sides: $ x^2 - 22 - (-2x + 26) = -2x + 26 - (-2x + 26)$ $ x^2 - 22 + 2x - 26 = 0$ $ x^2 - 48 + 2x = 0$ Factor the expression: $ (x + 8)(x - 6) = 0$ Therefore $x = -8$ or $x = 6$ However, the original expression is undefined when $x = -8$. Therefore, the only solution is $x = 6$.